> 数学 >
若x1、x2是方程2x2+5x-1=0的两个根,求下列各式的值:
(1)(x1-1)(x2-1);
(2)
x2
x1
+
x1
x2
人气:170 ℃ 时间:2019-10-26 19:52:34
解答
根据题意得x1+x2=-
5
2
,x1x2=-
1
2

(1)原式=x1x2-(x1+x2)+1
=-
1
2
+
5
2
+1
=3;
(2)原式=
x12+x22
x1x2
=
(x1+x2)2−2x1x2
x1x2

=
(−
5
2
)2−2×(−
1
2
)
1
2

=-
29
2
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